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Intelligent prediction of rockburst based on Copula-MC oversampling architecture

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Abstract

An unbalanced rockburst dataset will restrict the accuracy and reliability of rockburst prediction based on machine learning. Therefore, a new oversampling algorithm was proposed based on Copula theory and Monte Carlo simulation to balance the dataset. This paper collected 243 rockburst cases worldwide. The predictors of rockburst used in this paper include the maximum tangential stress of the surrounding rock, the uniaxial compressive strength of rock, the tensile strength of rock, and the elastic energy index. During oversampling, Copula theory determined the predictors' joint distribution function by considering the correlation among predictors. Then Monte Carlo simulation was performed to generate enough data for oversampling according to rockburst classification standard. Six common machine learning methods with tenfold cross-validation were adopted to establish nonlinear models between predictors and rockburst grades. The accuracy rate of rockburst prediction has increased by 9.3–15.5% after oversampling. The prediction performance is better than the commonly used synthetic minority oversampling technique. Finally, rockburst predictors' importance was evaluated with the initial dataset, and the elastic energy index got the maximum value of 0.41. The proposed oversampling algorithm in this paper can reasonably overcome class imbalance and improve the prediction performance for rockburst.

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Abbreviations

Copula-MC:

Copula theory and Monte Carlo simulation

SMOTE:

synthetic minority oversampling technique

σ θ :

the maximum tangential stress of the surrounding rock

σ c :

the unitial compressive strength of rock

σ t :

the tensile strength of rock

W et :

the elastic energy index

σ θ/σ c :

the stress ratio

σ c/σ t :

the rock brittleness ratio

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Acknowledgements

Research in this paper is supported by the National Natural Science Foundations of China (grant numbers 41877239, 51379112, 51422904, 40902084, and 41772298), Fundamental Research Funds of Shandong University (grant number 2018JC044), and Shandong Provincial Natural Science Foundation (grant number JQ201513).

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  1. Guangkun Li and Yiguo Xue contributed equally.

Authors and Affiliations

  1. Geotechnical and Structural Engineering Research Center, Shandong University, Ji’nan 250061, China

    Yiguo Xue, Guangkun Li, Zhiqiang Li, Peng Wang, Huimin Gong & Fanmeng Kong

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  1. Yiguo Xue
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Contributions

Yiguo Xue contributed to supervision, project administration, and funding acquisition. Guangkun Li contributed to conceptualization, methodology, writing—original draft, writing—review and editing, software, and investigation. Zhiqiang Li performed data curation. Peng Wang performed validation. Huimin Gong performed investigation. Fanmeng Kong carried out formal analysis.

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Correspondence to Yiguo Xue.

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Xue, Y., Li, G., Li, Z. et al. Intelligent prediction of rockburst based on Copula-MC oversampling architecture. Bull Eng Geol Environ 81, 209 (2022). https://doi.org/10.1007/s10064-022-02659-2

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